Remember that if you make purchases on the same card, your payments will be credited toward the balance with the lowest interest rate. So the 0% balance will drop with each payment, but the 10+% balance will rise with every purchase.
You need to be very careful with these things.
I have seen (still one on my desk now) zero interest, 3% fees, or 3% interest, zero fees, but not both zero.
I doubt such exists, or if it does exist, then they have found some other way to -ensure- that they get paid, not just hope you trip up and leak money to them.